Question

select all of the equations below that are equivalent to:
18 = -27r
use properties of equality.
-2·18 = 54r 3·18 = -81r
2·18 = -54r 54 = -27r·3

Explanation:

Step1: Recall equality property

If $a=b$, then $ka=kb$ for any $k$.

Step2: Test first equation

Multiply original by -2:
$-2\cdot18=-2\cdot(-27r) \implies -2\cdot18=54r$
This matches the first option.

Step3: Test second equation

Multiply original by 3:
$3\cdot18=3\cdot(-27r) \implies 3\cdot18=-81r$
This matches the second option.

Step4: Test third equation

Multiply original by 2:
$2\cdot18=2\cdot(-27r) \implies 2\cdot18=-54r$
This matches the third option.

Step5: Test fourth equation

Multiply original by 3:
$3\cdot18=3\cdot(-27r) \implies 54=-27r\cdot3$
This matches the fourth option.

Answer:

• $-2 \cdot 18 = 54r$
• $3 \cdot 18 = -81r$
• $2 \cdot 18 = -54r$
• $54 = -27r \cdot 3$